Activity: Diceware Passphrases

An exercise creating passphrases using the EFF's long improved-usability list.

For this activity, you will calculate the strength of a five-word Diceware passphrase in terms of the time and money required to crack it.

The Diceware system uses five six-sided dice to randomly select words from a wordlist of 7,776 words. 7,776 equals the number of sides on one dice, raised to the number of dice rolled together (65 = 7,776). This way, every roll of the five dice randomly selects a word from the list. Read more about Diceware here.

The EFF has created a set of Diceware lists that are easier to use. For this activity, use the EFF’s “long” improved-usability list, which also has 7,776 words, but which are easier to type and remember.

Questions

  1. Using five dice (either physcial dice or virtual dice at random.org) and the EFF’s instructions for generating passwords using dice, create two five-word Diceware passphrases. What passphrases did you create?

  2. What is the amount of entropy in bits for your five-word Diceware passphrases? How many possible passwords does that represent? Show your work.

    Note: Each Diceware word is worth an additional 12.9 bits of entropy. This is because 212.9 ≈ 7776, the length of the Diceware word list.

  3. On average, how long in hours would it take to guess a five-word Diceware passphrase if you could try 1 billion passwords a second? How many years? Show your work.

    Note: The average of a uniform distribution is half the numbers in a set.

  4. An Amazon EC2 p3.16xlarge high-performance computer can try 76,920 master passwords a second for the 1Password password manager.1 About how many of these computers would you need to rent in order to try 1 billion 1Password master passwords a second?

  5. One Amazon EC2 p3.16xlarge computer costs $24.48 an hour to rent as of February 2023. Guessing at the rate of 1 billion passwords a second, on average how much would it cost you to rent enough of these computers to crack a 1Password master password that uses a five-word Diceware passphrase?2

    In other words:

    (# of hours from answer to Question 2) * (# computers from answer to Question 4) * $24.48 an hour = Total cost in $

  6. What does Diceware have to do with Kerckhoff’s principle and Shannon’s maxim?

  7. How usable/memorable do you think Diceware passphrases are?

Footnotes

  1. Iraklis Mathiopoulos’ p3.16xlarge Hashcat benchmarks showed that it can guess 192.3 thousand 1Password master passwords a second at 40,000 iterations (hash mode 8200). However, 1Password now uses a slow hashing algorithm (PBKDF2-HMAC-SHA256) to hash the master password with 100,000 iterations, or about 2.5 slower than the Hashcat benchmark. 192,300 / 2.5 = 76,920. ↩

  2. This question is inspired by Micah Flee’s calculations here. ↩